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Cited by 108Computational Fluid Dynamics and AerodynamicsAquatic and Environmental StudiesNonlinear Waves and Solitons

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Finite-volume schemes for shallow-water equations

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Kurganov, Alexander·2018·Acta Numerica
DOI 10.1017/s0962492918000028
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Abstract

Shallow-water equations are widely used to model water flow in rivers, lakes, reservoirs, coastal areas, and other situations in which the water depth is much smaller than the horizontal length scale of motion. The classical shallow-water equations, the Saint-Venant system, were originally proposed about 150 years ago and still are used in a variety of applications. For many practical purposes, it is extremely important to have an accurate, efficient and robust numerical solver for the Saint-Venant system and related models. As their solutions are typically non-smooth and even discontinuous, finite-volume schemes are among the most popular tools. In this paper, we review such schemes and focus on one of the simplest (yet highly accurate and robust) methods: central-upwind schemes. These schemes belong to the family of Godunov-type Riemann-problem-solver-free central schemes, but incorporate some upwinding information about the local speeds of propagation, which helps to reduce an excessive amount of numerical diffusion typically present in classical (staggered) non-oscillatory central schemes. Besides the classical one- and two-dimensional Saint-Venant systems, we will consider the shallow-water equations with friction terms, models with moving bottom topography, the two-layer shallow-water system as well as general non-conservative hyperbolic systems.

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Metadata

Authors
Kurganov, A.
Affiliations
Tulane University (US)
Corresponding author
Kurganov, Alexander
ORCID
Kurganov, Alexander
Venue
Acta Numerica
Publisher
Cambridge University Press (CUP)
Published
2018-05-01
Volume
27
Pages
289-351
ISSN
  • 0962-4929 (ISSN-L)
  • 1474-0508
DOI
10.1017/s0962492918000028
OpenAlex
W2799904623
Cited by
108
References
0
Citations by year
2026: 9 · 2025: 18 · 2024: 15 · 2023: 17 · 2022: 18 · 2021: 13 · 2020: 15 · 2019: 2 · 2018: 1
FWCI
5.58
Type
journal article
Language
en
Open access
Licence
www.cambridge.org/core/terms (unspecified, 3 d)
Locations
Acta Numerica (publishedVersion)
Topics
  • Physical Sciences › Engineering › Computational Mechanics › Computational Fluid Dynamics and Aerodynamics
  • Physical Sciences › Earth and Planetary Sciences › Earth-Surface Processes › Aquatic and Environmental Studies
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Waves and Solitons
Keywords
shallow water equations, Saint-Venant system, finite volume method, central-upwind schemes, Godunov-type schemes, Riemann solvers, numerical diffusion, friction term, non-conservative hyperbolic systems, non-smooth solutions

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CoChat. (2026). Citation check: Finite-volume schemes for shallow-water equations. https://app.cochat.ai/papers/10.1017/s0962492918000028
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Kurganov, A. (2018). Finite-volume schemes for shallow-water equations. Acta Numerica. https://doi.org/10.1017/s0962492918000028